In Gauge Mediated SUSY breaking scenarios, the gravitino mass gives direct access to the scale of the SUSY breaking, and can potentially contribute to the total amount of Dark Matter in the Universe. In this section, the monojet results are interpreted in the context of gravitino production in association with a squark or a gluino in the final state. Figure 3.3 shows some of the Feynman diagrams for this process. A simplified SUSY model is used for which the squark or the gluino decays to a gravitino, and a quark or a gluon in the final state (see Figure 3.2), thus leading to a monojet signature.
Monte Carlo samples corresponding to gravitino production in associ-ation with a gluino or a squark in the final state, pp → q˜G˜ + X and pp → g˜G˜ + X are generated at LO using Madgraph, interfaced with Pythiafor the showering. The ATLAS detector simulation is provided by the ATLAS fast simulation, while the PDF set used is CTEQ6L1. The renor-malization and factorization scales are set to the average of the mass of the final state particles involved in the hard interaction (mG˜+mq,˜˜g)/2'mq,˜˜g)/2.
A grid with different mass configurations has been generated with mq,˜˜g
from 50 GeV to 2.6 TeV andmq˜/m˜g= 0.25,0.5,1,2,4, and a gravitino mass mG˜ = 5×10−4eV. Both experimental and theoretical systematic uncertain-ties for the different mass configurations are computed as for the previous models discussed in Section 8.4. Experimental uncertainties result into a 4.6% to 2.9% effect on the signal yield in M3, and a 16% to 3% effect in M6 for squark and gluino masses of 200 GeV and 2.4 TeV, respectively. The the-oretical uncertainties on the acceptance introduce a variation in the signal yield of about 15%, while the theoretical uncertainties on the cross section contribute altogether to a 24% to 55% on the signal yield for different squark and gluino masses.
10.2. GRAVITINO PRODUCTION IN GMSB 159 10.2.1 Exclusion Limits at 95% CL
In this case, the 95% CL limits on the visible cross section of the monojet analysis shown in Table 8.1 are used to extract the limits on the gravitino mass as a function of the masses of the squark or the gluinos. The best sensitivity to the gravitino production is obtained for the selections M3, M5 and M6, and depends on the squark and gluino mass configuration.
Figure 10.5 shows, for the signal region M5, the fiducial cross section as a function of the squark and gluino mass, for different gravitino masses. For comparison, the model independent limits from Table 8.1 are shown. The intersection between the model independent limit and the signal fiducial cross section determines the exclusion in terms of the parameters of the model. The following limits are calculated:
• Observed: intersection between the observed model independent limit and the signal visible cross section.
• Observed−1σtotalsignal: intersection between the observed model indepen-dent limit and the signal visible cross section−1σ of the total uncer-tainty on the signal. The total unceruncer-tainty is computed by summing in quadrature the experimental uncertainties and both the theoretical uncertainties on the acceptance and on the cross section.
• Observed −1σexpsignal: intersection between the observed limit and the signal visible cross section−1σ of the experimental uncertainty on the signal together with the effects of the modeling uncertainty on the signal acceptance (no cross section uncertainty is considered in this case).
• Expected: intersection between the expected model independent limit and the signal visible cross section.
• Expected ±1σ or ±2σ: intersection between the signal visible cross section and the expected limit with ±1σ or ±2σ experimental uncer-tainty on the Standard Model background.
This approach does not take into account the correlations between the signal and the background uncertainties. The CLs computation for each of the mass configurations in the grid would require a huge computational power, thus making the analysis very time consuming. Tests performed for several cases showed that the exclusions using the model independent limits or using theCLs method return compatible, almost identical, results.
Figure 10.6 shows the 95% CL limits on the gravitino mass, mG˜, for equal squark and gluino masses. Gravitino masses below 3.5 ×10−4 eV, 3×104eV and 2×10−4eV are excluded at 95% CL for squark/gluino masses of 500 GeV, 1 TeV and 1.5 TeV. For very high squark/gluino masses the
narrow-width approximation (NWA) employed is violated since the partial width for the gluino and squark to decay into a gravitino and a parton becomes more than 25% of its mass. In this case, other decay channels for the gluino and squarks should be considered, leading to a different final state.
Figures 10.7 and 10.8 show the limits on the gravitino mass, form˜g= 2×mq˜
and m˜g = 4×mq˜; and mg˜ =mq˜/2 and m˜g = mq˜/4, respectively. In this case, lower bounds on gravitino mass in the range between 5×10−4 and 5×10−5 are set depending on the squark and gluino masses.
The limits on the gravitino mass shown in Figures 10.6 to 10.8 can be translated into 95% CL upper limits on the breaking scale of SUSY,p
hFi.
These limits are shown in Figures 10.9 to 10.11, for the different squark and gluino mass configurations. Values of the p
hFi below 1 TeV can be excluded for squark/gluino masses of 1 TeV.
10.2. GRAVITINO PRODUCTION IN GMSB 161
mχ[GeV]M∗ D5(vector)M∗ D8(axial-vector)M∗ D9(tensor) Obs.[GeV]Exp.[GeV]Obs.[GeV]Exp.[GeV]Obs.[GeV]Exp.[GeV] 199099297197316721677 1099099297197316721677 5099099297197317151719 10097998294895016131618 20095796089389315411545 40089689976076312941297 700706708544545922923 1000507509367369634636 1300344345229230430431 Table10.1:The90%CLobservedandexpectedlimitsonM∗ asafunctionoftheWIMPmassmχforD5(vector),D8 (axial-vector)andD9(tensor)interactionmodels.
mχ [GeV] M∗ [GeV] D5 (vector) M∗ [GeV] D9 (tensor)
1 600
-10 650 1600
25 650
-50 600 1650
100 550 1550
200 - 1450
Table 10.2: 90% CL Observed limit on M∗ for D5 and D9 models, with truncation of the events with√
ˆ s > M∗.
10.2. GRAVITINO PRODUCTION IN GMSB 163
mχ[GeV]σχN(D5)σχN(D8)σχN(D9) Obs.[GeV]Exp.[cm2]Obs.[cm2]Exp.[cm2]Obs.[cm2]Exp.[cm2] 12.73×10−40 2.71×10−40 1.00×10−41 9.95×10−42 1.14×10−42 1.13×10−42 108.56×10−40 8.49×10−40 3.15×10−41 3.13×10−41 3.58×10−42 3.54×10−42 509.87×10−40 9.79×10−40 3.63×10−41 3.60×10−41 3.73×10−42 3.70×10−42 1001.05×10−39 1.04×10−39 4.07×10−41 4.04×10−41 4.86×10−42 4.80×10−42 2001.16×10−39 1.15×10−39 5.22×10−41 5.17×10−41 5.89×10−42 5.83×10−42 4001.52×10−39 1.50×10−39 1.00×10−40 9.84×10−41 1.19×10−41 1.18×10−41 7003.95×10−39 3.91×10−39 3.81×10−40 3.79×10−40 4.63×10−41 4.61×10−41 10001.49×10−38 1.46×10−38 1.84×10−39 1.80×10−39 2.07×10−40 2.05×10−40 13007.02×10−38 6.94×10−38 1.22×10−38 1.20×10−38 9.79×10−40 9.70×10−40 Table10.3:The90%CLobservedandexpectedlimitsontheWIMP-Nucleonscatteringcross-sectionσχNasafunctionof theWIMPmassmχforD5(vector),D8(axial-vector)andD9(tensor)interactionmodels.
mχ [GeV] σχN(D5) σχN(D9)
1 2.02×10−39
-10 4.61×10−39 4.27×10−42
25 5.12×10−39
-50 7.31×10−39 4.36×10−42 100 1.06×10−38 5.70×10−42
200 - 7.51×10−42
Table 10.4: The 90% CL Observed limit on WIMP-nucleon cross section, σχ−N, for D5 and D9 models, with truncation of the events with√
ˆ
s > M∗.
10.2. GRAVITINO PRODUCTION IN GMSB 165
[GeV]
WIMP mass mχ
1 10 102 103
]2WIMP-nucleon cross section [cm
10-46
]2WIMP-nucleon cross section [cm
10-44
Figure 10.4: The 90% CL lower limits on independent (top) and spin-dependent (bottom) WIMP-nucleon scattering cross section for different masses ofχ in M3 signal region. Results from direct detection experiments for the independent [56, 104, 55, 105, 106, 107, 54, 58, 108] and spin-dependent [109, 110, 111, 112, 113] cross section, and the CMS (untruncated) limits [114] are also shown for comparison.
[GeV]
g~ / q~
0 500 1000 1500 2000 2500 3000m 3500
[pb]∈× A ×σ function of the squark/gluino mass for degenerate squark and gluinos in the signal region M5. Different values of the gravitino mass are considered and the predictions are compared to the model independent limits (see Table 8.1).
10.2. GRAVITINO PRODUCTION IN GMSB 167
[GeV]
g~ / q~
0 500 1000 1500 2000 2500m 3000
[eV] G~m
10-7
10-6
10-5
10-4
10-3
q~ = m g~ 95% CL M3+M5+M6, m
Observed limit limit signal total Observed -1σ
limit signal σexp Observed -1 Expected limit
σexp 1
± σexp 2
± NWA limit
Ldt=20.3 fb-1
∫
= 8 TeV s
R. Caminal − PhD Thesis
Figure 10.6: Observed (solid line) and expected (dashed line) 95% CL lower limits on the gravitino mass as a function of the squark mass for equal squark and neutralino masses. The dotted line indicates the impact on the observed limit of the±1σ LO theoretical uncertainty. The shaded bands around the expected line indicate the expected ±1σ and ±2σ ranges of limits. The region above the black dotted line defines the validity of the narrow-width approximation (NWA) for which the decay width is smaller than 25% of the squark/gluino mass.
[GeV]
g~
0 500 1000 1500 2000 2500m 3000
[eV] G~m
0 500 1000 1500 2000 2500 3000
[eV] G~m
Figure 10.7: Observed (solid line) and expected (dashed line) 95% CL lower limits on the gravitino mass as a function of the squark mass form˜g= 2×mq˜ (top) and mg˜ = 4×mq˜ (bottom). The dotted line indicates the impact on the observed limit of the ±1σ LO theoretical uncertainty. The shaded bands around the expected line indicate the expected±1σ and ±2σ ranges of limits. The region above the black dotted line defines the validity of the narrow-width approximation (NWA) for which the decay width is smaller than 25% of the squark/gluino mass.
10.2. GRAVITINO PRODUCTION IN GMSB 169
Figure 10.8: Observed (solid line) and expected (dashed line) 95% CL lower limits on the gravitino mass as a function of the squark mass for m˜g = 1/2×mq˜(top) andm˜g= 1/4×mq˜(bottom). The dotted line indicates the impact on the observed limit of the ±1σ LO theoretical uncertainty. The shaded bands around the expected line indicate the expected±1σ and±2σ ranges of limits. The region above the black dotted line defines the validity of the narrow-width approximation (NWA) for which the decay width is smaller than 25% of the squark/gluino mass.
[GeV]
g~ / q~
0 500 1000 1500 2000 2500m 3000
[GeV]〉F〈
102
103
q~ = m g~ 95% CL M3+M5+M6, m
Observed limit limit signal total Observed -1σ
limit signal σexp Observed -1 Expected limit
σexp 1
± σexp 2
± NWA limit
Ldt=20.3 fb-1
∫
= 8 TeV s
R. Caminal − PhD Thesis
Figure 10.9: Observed (solid line) and expected (dashed line) 95% CL lower limits on the SUSY breaking scale F as a function of the squark mass for equal squark and neutralino masses. The dotted line indicates the impact on the observed limit of the ±1σ LO theoretical uncertainty. The shaded bands around the expected line indicate the expected±1σ and ±2σ ranges of limits. The region above the black dotted line defines the validity of the narrow-width approximation (NWA) for which the decay width is smaller than 25% of the squark/gluino mass.
10.2. GRAVITINO PRODUCTION IN GMSB 171
[GeV]
g~
0 500 1000 1500 2000 2500m 3000
[GeV]〉F〈 95% CL A4+A9+A10, m Observed limit
0 500 1000 1500 2000 2500 3000
[GeV]〉F〈
Figure 10.10: Observed (solid line) and expected (dashed line) 95% CL lower limits on the SUSY breaking scale F as a function of the squark mass for mg˜= 2×mq˜(top) andmg˜= 4×mq˜(bottom). The dotted line indicates the impact on the observed limit of the ±1σ LO theoretical uncertainty. The shaded bands around the expected line indicate the expected±1σ and±2σ ranges of limits. The region above the black dotted line defines the validity of the narrow-width approximation (NWA) for which the decay width is smaller than 25% of the squark/gluino mass.
[GeV]
Figure 10.11: Observed (solid line) and expected (dashed line) 95% CL lower limits on the SUSY breaking scale F as a function of the squark mass for m˜g = 1/2×mq˜(top) andm˜g= 1/4×mq˜(bottom). The dotted line indicates the impact on the observed limit of the±1σLO theoretical uncertainty. The shaded bands around the expected line indicate the expected±1σ and ±2σ ranges of limits. The region above the black dotted line defines the validity of the narrow-width approximation (NWA) for which the decay width is smaller than 25% of the squark/gluino mass.
Chapter 11
Interpretations: ADD Large Extra Dimensions
This chapter presents the results of the monojet analysis interpreted in the context of the LED ADD scenario discussed in Section 3.3. This model postulates the presence of n extra spacial dimensions of size R, with only the graviton field being able to propagate through them. This results in a reduction of the gravitational strength, with MD, the fundamental Planck scale in 4 +ndimensions, close to the electroweak scale for large enough R, and thus solving the hierarchy problem. The agreement between the data and the MC background simulation for the selections M1 to M6 is translated into 95% CL limits on the parameters of this model.
11.1 ADD LED signal samples and systematic un-certainties on the signal
Monte Carlo samples for differentnandMDparameter configurations of the ADD LED model, are generated usingExoGraviton i1 and the CTEQ6.6 PDFs set. The renormalization and factorization scales are set to
q
m2G/2 +p2T, where mG is the graviton mass and pT denotes the transverse momentum of the recoiling parton [115].
Different sources of systematic uncertainties on the ADD signals are considered, as detailed in Section 8.4 for the case of third generation SUSY searches. Experimental uncertainties include: uncertainties on the jet and ETmiss energy scales and resolutions; uncertainties on the simulated lepton identification, energy scales and resolutions; and the uncertainty on the total integrated luminosity. The uncertainty on the PDFs; the uncertainty on the factorization, renormalization and matching scales; and the uncertainty on
1ExoGraviton iis a dedicated module ofPythia8
173
the initial- and final-state gluon radiation constitute the theoretical uncer-tainties, that affect both the acceptance and the cross section of the model.
The theoretical uncertainties on the acceptance introduce a 10% effect on the total signal yield, inspired by the previous studies found in Ref. [115].
This reference also provides a computation for the theoretical uncertainty on the cross section, which is also adopted for this analysis. This uncertainty results into a 36% to 62% in all the signal regions forn increasing from 2 to 6.